Given the potential barrier, \begin{align} V(x, y) = \left\{ \begin{array}{cc} V_{0} & \hspace{5mm} \text{if $0 \leq x \leq D$} \\ 0 & \hspace{5mm} \text{otherwise} \end{array} \right. \end{align}
the Hamiltonian of the system is $$\hat H = -\frac{\hbar^{2}}{2m}\nabla^{2}+V$$
Hence for $x<0$, the time-independent wavefunction is: $$\Psi(x) = A\,exp(ikx)+B\, exp(-ikx)$$
This is an eigenvector of $\hat H$ with the first term representing the incident wave while the second term represents the reflected wave.
Now for this region $[\hat H, \hat p]=0$, so they should have common non-degenerate eigenvectors.
But the above wavefunction is not an eigenvector of $\hat p$. What am I thinking wrong here?